Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.7%

Time: 13.0s

Alternatives: 15

Speedup: 1.2×

• 21.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (+ (* -6.0 (* z (- y x))) (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((-6.0d0) * (z * (y - x))) + ((y - x) * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

Python

def code(x, y, z):
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(-6.0 * Float64(z * Float64(y - x))) + Float64(Float64(y - x) * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 99.8%

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

6. Final simplification 99.8%

   \[\leadsto x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \]
7. Add Preprocessing

Alternative 2: 51.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -560:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-136}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -560.0)
     t_0
     (if (<= z -7.8e-76)
       (* y 4.0)
       (if (<= z -1.45e-136)
         (* x -3.0)
         (if (<= z -2.2e-198)
           (* y 4.0)
           (if (<= z -4.5e-262)
             (* x -3.0)
             (if (<= z -1.22e-284)
               (* y 4.0)
               (if (<= z 4.2e-205)
                 (* x -3.0)
                 (if (<= z 0.63)
                   (* y 4.0)
                   (if (<= z 1.05e+72) t_0 (* -6.0 (* z y)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -560.0) {
		tmp = t_0;
	} else if (z <= -7.8e-76) {
		tmp = y * 4.0;
	} else if (z <= -1.45e-136) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-198) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-262) {
		tmp = x * -3.0;
	} else if (z <= -1.22e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-205) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else if (z <= 1.05e+72) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-560.0d0)) then
        tmp = t_0
    else if (z <= (-7.8d-76)) then
        tmp = y * 4.0d0
    else if (z <= (-1.45d-136)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.2d-198)) then
        tmp = y * 4.0d0
    else if (z <= (-4.5d-262)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.22d-284)) then
        tmp = y * 4.0d0
    else if (z <= 4.2d-205) then
        tmp = x * (-3.0d0)
    else if (z <= 0.63d0) then
        tmp = y * 4.0d0
    else if (z <= 1.05d+72) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -560.0) {
		tmp = t_0;
	} else if (z <= -7.8e-76) {
		tmp = y * 4.0;
	} else if (z <= -1.45e-136) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-198) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-262) {
		tmp = x * -3.0;
	} else if (z <= -1.22e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-205) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else if (z <= 1.05e+72) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -560.0:
		tmp = t_0
	elif z <= -7.8e-76:
		tmp = y * 4.0
	elif z <= -1.45e-136:
		tmp = x * -3.0
	elif z <= -2.2e-198:
		tmp = y * 4.0
	elif z <= -4.5e-262:
		tmp = x * -3.0
	elif z <= -1.22e-284:
		tmp = y * 4.0
	elif z <= 4.2e-205:
		tmp = x * -3.0
	elif z <= 0.63:
		tmp = y * 4.0
	elif z <= 1.05e+72:
		tmp = t_0
	else:
		tmp = -6.0 * (z * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -560.0)
		tmp = t_0;
	elseif (z <= -7.8e-76)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.45e-136)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.2e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.5e-262)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.22e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.2e-205)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.63)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.05e+72)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -560.0)
		tmp = t_0;
	elseif (z <= -7.8e-76)
		tmp = y * 4.0;
	elseif (z <= -1.45e-136)
		tmp = x * -3.0;
	elseif (z <= -2.2e-198)
		tmp = y * 4.0;
	elseif (z <= -4.5e-262)
		tmp = x * -3.0;
	elseif (z <= -1.22e-284)
		tmp = y * 4.0;
	elseif (z <= 4.2e-205)
		tmp = x * -3.0;
	elseif (z <= 0.63)
		tmp = y * 4.0;
	elseif (z <= 1.05e+72)
		tmp = t_0;
	else
		tmp = -6.0 * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -560.0], t$95$0, If[LessEqual[z, -7.8e-76], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.45e-136], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.2e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.5e-262], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.22e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.2e-205], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.63], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.05e+72], t$95$0, N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -560 or 0.630000000000000004 < z < 1.0500000000000001e72

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 61.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 61.3%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 61.3%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 61.3%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 61.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 61.3%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 61.3%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 61.3%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 61.3%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 61.3%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 61.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 56.3%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   9. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -560 < z < -7.8000000000000005e-76 or -1.44999999999999997e-136 < z < -2.2e-198 or -4.49999999999999998e-262 < z < -1.22e-284 or 4.19999999999999965e-205 < z < 0.630000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 67.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 63.5%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -7.8000000000000005e-76 < z < -1.44999999999999997e-136 or -2.2e-198 < z < -4.49999999999999998e-262 or -1.22e-284 < z < 4.19999999999999965e-205

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 1.0500000000000001e72 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot \left(0.6666666666666666 - z\right)}{x}\right)} \]

   7. Taylor expanded in z around inf 71.9%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -560:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-136}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+72}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -275:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-68}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-279}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -275.0)
     t_0
     (if (<= z -3.4e-68)
       (* y 4.0)
       (if (<= z -1.85e-131)
         (* x -3.0)
         (if (<= z -4.9e-197)
           (* y 4.0)
           (if (<= z -5.8e-263)
             (* x -3.0)
             (if (<= z -1.3e-279)
               (* y 4.0)
               (if (<= z 3.2e-206)
                 (* x -3.0)
                 (if (<= z 0.54)
                   (* y 4.0)
                   (if (<= z 7.5e+71) t_0 (* y (* -6.0 z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -275.0) {
		tmp = t_0;
	} else if (z <= -3.4e-68) {
		tmp = y * 4.0;
	} else if (z <= -1.85e-131) {
		tmp = x * -3.0;
	} else if (z <= -4.9e-197) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-263) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-279) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else if (z <= 7.5e+71) {
		tmp = t_0;
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-275.0d0)) then
        tmp = t_0
    else if (z <= (-3.4d-68)) then
        tmp = y * 4.0d0
    else if (z <= (-1.85d-131)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.9d-197)) then
        tmp = y * 4.0d0
    else if (z <= (-5.8d-263)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.3d-279)) then
        tmp = y * 4.0d0
    else if (z <= 3.2d-206) then
        tmp = x * (-3.0d0)
    else if (z <= 0.54d0) then
        tmp = y * 4.0d0
    else if (z <= 7.5d+71) then
        tmp = t_0
    else
        tmp = y * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -275.0) {
		tmp = t_0;
	} else if (z <= -3.4e-68) {
		tmp = y * 4.0;
	} else if (z <= -1.85e-131) {
		tmp = x * -3.0;
	} else if (z <= -4.9e-197) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-263) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-279) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else if (z <= 7.5e+71) {
		tmp = t_0;
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -275.0:
		tmp = t_0
	elif z <= -3.4e-68:
		tmp = y * 4.0
	elif z <= -1.85e-131:
		tmp = x * -3.0
	elif z <= -4.9e-197:
		tmp = y * 4.0
	elif z <= -5.8e-263:
		tmp = x * -3.0
	elif z <= -1.3e-279:
		tmp = y * 4.0
	elif z <= 3.2e-206:
		tmp = x * -3.0
	elif z <= 0.54:
		tmp = y * 4.0
	elif z <= 7.5e+71:
		tmp = t_0
	else:
		tmp = y * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -275.0)
		tmp = t_0;
	elseif (z <= -3.4e-68)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.85e-131)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.9e-197)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.8e-263)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.3e-279)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.2e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.54)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.5e+71)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -275.0)
		tmp = t_0;
	elseif (z <= -3.4e-68)
		tmp = y * 4.0;
	elseif (z <= -1.85e-131)
		tmp = x * -3.0;
	elseif (z <= -4.9e-197)
		tmp = y * 4.0;
	elseif (z <= -5.8e-263)
		tmp = x * -3.0;
	elseif (z <= -1.3e-279)
		tmp = y * 4.0;
	elseif (z <= 3.2e-206)
		tmp = x * -3.0;
	elseif (z <= 0.54)
		tmp = y * 4.0;
	elseif (z <= 7.5e+71)
		tmp = t_0;
	else
		tmp = y * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -275.0], t$95$0, If[LessEqual[z, -3.4e-68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.85e-131], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.9e-197], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.8e-263], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.3e-279], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.2e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.5e+71], t$95$0, N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -275 or 0.54000000000000004 < z < 7.50000000000000007e71

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 61.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 61.3%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 61.3%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 61.3%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 61.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 61.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 61.3%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 61.3%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 61.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 61.3%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 61.3%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 61.3%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 61.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 56.3%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   9. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -275 < z < -3.40000000000000018e-68 or -1.8500000000000001e-131 < z < -4.9000000000000002e-197 or -5.80000000000000007e-263 < z < -1.3000000000000001e-279 or 3.19999999999999976e-206 < z < 0.54000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 67.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 63.5%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -3.40000000000000018e-68 < z < -1.8500000000000001e-131 or -4.9000000000000002e-197 < z < -5.80000000000000007e-263 or -1.3000000000000001e-279 < z < 3.19999999999999976e-206

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 7.50000000000000007e71 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot \left(0.6666666666666666 - z\right)}{x}\right)} \]

   7. Taylor expanded in z around inf 71.9%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

      2. *-commutative 71.9%

         \[\leadsto \color{blue}{\left(y \cdot -6\right)} \cdot z \]

      3. associate-*l* 72.0%

         \[\leadsto \color{blue}{y \cdot \left(-6 \cdot z\right)} \]

   9. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -275:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-68}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-279}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -310:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-73}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-275}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-204}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -310.0)
   (* 6.0 (* x z))
   (if (<= z -9.2e-73)
     (* y 4.0)
     (if (<= z -2.5e-135)
       (* x -3.0)
       (if (<= z -1.1e-197)
         (* y 4.0)
         (if (<= z -3e-264)
           (* x -3.0)
           (if (<= z -2.8e-275)
             (* y 4.0)
             (if (<= z 9.6e-204)
               (* x -3.0)
               (if (<= z 0.6)
                 (* y 4.0)
                 (if (<= z 6e+72) (* z (* x 6.0)) (* y (* -6.0 z))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -310.0) {
		tmp = 6.0 * (x * z);
	} else if (z <= -9.2e-73) {
		tmp = y * 4.0;
	} else if (z <= -2.5e-135) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-197) {
		tmp = y * 4.0;
	} else if (z <= -3e-264) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-275) {
		tmp = y * 4.0;
	} else if (z <= 9.6e-204) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 6e+72) {
		tmp = z * (x * 6.0);
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-310.0d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-9.2d-73)) then
        tmp = y * 4.0d0
    else if (z <= (-2.5d-135)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.1d-197)) then
        tmp = y * 4.0d0
    else if (z <= (-3d-264)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.8d-275)) then
        tmp = y * 4.0d0
    else if (z <= 9.6d-204) then
        tmp = x * (-3.0d0)
    else if (z <= 0.6d0) then
        tmp = y * 4.0d0
    else if (z <= 6d+72) then
        tmp = z * (x * 6.0d0)
    else
        tmp = y * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -310.0) {
		tmp = 6.0 * (x * z);
	} else if (z <= -9.2e-73) {
		tmp = y * 4.0;
	} else if (z <= -2.5e-135) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-197) {
		tmp = y * 4.0;
	} else if (z <= -3e-264) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-275) {
		tmp = y * 4.0;
	} else if (z <= 9.6e-204) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 6e+72) {
		tmp = z * (x * 6.0);
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -310.0:
		tmp = 6.0 * (x * z)
	elif z <= -9.2e-73:
		tmp = y * 4.0
	elif z <= -2.5e-135:
		tmp = x * -3.0
	elif z <= -1.1e-197:
		tmp = y * 4.0
	elif z <= -3e-264:
		tmp = x * -3.0
	elif z <= -2.8e-275:
		tmp = y * 4.0
	elif z <= 9.6e-204:
		tmp = x * -3.0
	elif z <= 0.6:
		tmp = y * 4.0
	elif z <= 6e+72:
		tmp = z * (x * 6.0)
	else:
		tmp = y * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -310.0)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -9.2e-73)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.5e-135)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.1e-197)
		tmp = Float64(y * 4.0);
	elseif (z <= -3e-264)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.8e-275)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.6e-204)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.6)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e+72)
		tmp = Float64(z * Float64(x * 6.0));
	else
		tmp = Float64(y * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -310.0)
		tmp = 6.0 * (x * z);
	elseif (z <= -9.2e-73)
		tmp = y * 4.0;
	elseif (z <= -2.5e-135)
		tmp = x * -3.0;
	elseif (z <= -1.1e-197)
		tmp = y * 4.0;
	elseif (z <= -3e-264)
		tmp = x * -3.0;
	elseif (z <= -2.8e-275)
		tmp = y * 4.0;
	elseif (z <= 9.6e-204)
		tmp = x * -3.0;
	elseif (z <= 0.6)
		tmp = y * 4.0;
	elseif (z <= 6e+72)
		tmp = z * (x * 6.0);
	else
		tmp = y * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -310.0], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-73], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.5e-135], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.1e-197], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3e-264], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.8e-275], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.6e-204], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e+72], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -310

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 56.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 56.2%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 56.2%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 56.2%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 56.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 56.2%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 56.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 56.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 56.2%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 56.2%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 56.2%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 56.2%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 56.2%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 56.2%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 56.2%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 56.2%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 56.2%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 56.2%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 56.2%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 54.4%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   9. Taylor expanded in x around 0 54.4%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -310 < z < -9.19999999999999953e-73 or -2.5000000000000001e-135 < z < -1.1e-197 or -3e-264 < z < -2.79999999999999994e-275 or 9.6e-204 < z < 0.599999999999999978

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 67.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 63.5%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -9.19999999999999953e-73 < z < -2.5000000000000001e-135 or -1.1e-197 < z < -3e-264 or -2.79999999999999994e-275 < z < 9.6e-204

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.599999999999999978 < z < 6.00000000000000006e72

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 74.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 74.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 74.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 74.7%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 74.7%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 74.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 74.7%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 74.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 74.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 74.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 74.7%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 74.7%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 74.7%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 74.7%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 74.7%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 74.7%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 74.7%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 74.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 74.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 74.7%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 74.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 61.2%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   9. Taylor expanded in x around 0 61.3%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 61.3%

          \[\leadsto 6 \cdot \color{blue}{\left(z \cdot x\right)} \]

       2. *-commutative 61.3%

          \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 6} \]

       3. associate-*r* 61.4%

          \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]

       4. *-commutative 61.4%

          \[\leadsto z \cdot \color{blue}{\left(6 \cdot x\right)} \]

   11. Simplified 61.4%

       \[\leadsto \color{blue}{z \cdot \left(6 \cdot x\right)} \]

   if 6.00000000000000006e72 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot \left(0.6666666666666666 - z\right)}{x}\right)} \]

   7. Taylor expanded in z around inf 71.9%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

      2. *-commutative 71.9%

         \[\leadsto \color{blue}{\left(y \cdot -6\right)} \cdot z \]

      3. associate-*l* 72.0%

         \[\leadsto \color{blue}{y \cdot \left(-6 \cdot z\right)} \]

   9. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -310:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-73}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-275}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-204}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.062:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.062)
     t_0
     (if (<= z -3.4e-76)
       (* y 4.0)
       (if (<= z -4.5e-133)
         (* x -3.0)
         (if (<= z -1.96e-197)
           (* y 4.0)
           (if (<= z -2.05e-262)
             (* x -3.0)
             (if (<= z -4e-279)
               (* y 4.0)
               (if (<= z 9.5e-206)
                 (* x -3.0)
                 (if (<= z 0.63) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.062) {
		tmp = t_0;
	} else if (z <= -3.4e-76) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-133) {
		tmp = x * -3.0;
	} else if (z <= -1.96e-197) {
		tmp = y * 4.0;
	} else if (z <= -2.05e-262) {
		tmp = x * -3.0;
	} else if (z <= -4e-279) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.062d0)) then
        tmp = t_0
    else if (z <= (-3.4d-76)) then
        tmp = y * 4.0d0
    else if (z <= (-4.5d-133)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.96d-197)) then
        tmp = y * 4.0d0
    else if (z <= (-2.05d-262)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4d-279)) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-206) then
        tmp = x * (-3.0d0)
    else if (z <= 0.63d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.062) {
		tmp = t_0;
	} else if (z <= -3.4e-76) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-133) {
		tmp = x * -3.0;
	} else if (z <= -1.96e-197) {
		tmp = y * 4.0;
	} else if (z <= -2.05e-262) {
		tmp = x * -3.0;
	} else if (z <= -4e-279) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.062:
		tmp = t_0
	elif z <= -3.4e-76:
		tmp = y * 4.0
	elif z <= -4.5e-133:
		tmp = x * -3.0
	elif z <= -1.96e-197:
		tmp = y * 4.0
	elif z <= -2.05e-262:
		tmp = x * -3.0
	elif z <= -4e-279:
		tmp = y * 4.0
	elif z <= 9.5e-206:
		tmp = x * -3.0
	elif z <= 0.63:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.062)
		tmp = t_0;
	elseif (z <= -3.4e-76)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.5e-133)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.96e-197)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.05e-262)
		tmp = Float64(x * -3.0);
	elseif (z <= -4e-279)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.63)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.062)
		tmp = t_0;
	elseif (z <= -3.4e-76)
		tmp = y * 4.0;
	elseif (z <= -4.5e-133)
		tmp = x * -3.0;
	elseif (z <= -1.96e-197)
		tmp = y * 4.0;
	elseif (z <= -2.05e-262)
		tmp = x * -3.0;
	elseif (z <= -4e-279)
		tmp = y * 4.0;
	elseif (z <= 9.5e-206)
		tmp = x * -3.0;
	elseif (z <= 0.63)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.062], t$95$0, If[LessEqual[z, -3.4e-76], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.5e-133], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.96e-197], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.05e-262], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4e-279], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.63], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.062 or 0.630000000000000004 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 94.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.062 < z < -3.3999999999999999e-76 or -4.50000000000000009e-133 < z < -1.9600000000000001e-197 or -2.05000000000000013e-262 < z < -4.00000000000000022e-279 or 9.49999999999999979e-206 < z < 0.630000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 65.0%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -3.3999999999999999e-76 < z < -4.50000000000000009e-133 or -1.9600000000000001e-197 < z < -2.05000000000000013e-262 or -4.00000000000000022e-279 < z < 9.49999999999999979e-206

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.062:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -4800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* z (- y x)))))
   (if (<= z -4800.0)
     t_1
     (if (<= z -2.5e-69)
       t_0
       (if (<= z -1.3e-131)
         (* x -3.0)
         (if (<= z -2.5e-197)
           (* y 4.0)
           (if (<= z -2.45e-262)
             (* x -3.0)
             (if (<= z -1.9e-284)
               (* y 4.0)
               (if (<= z 3.6e-205) (* x -3.0) (if (<= z 0.63) t_0 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -4800.0) {
		tmp = t_1;
	} else if (z <= -2.5e-69) {
		tmp = t_0;
	} else if (z <= -1.3e-131) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-197) {
		tmp = y * 4.0;
	} else if (z <= -2.45e-262) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-205) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * (z * (y - x))
    if (z <= (-4800.0d0)) then
        tmp = t_1
    else if (z <= (-2.5d-69)) then
        tmp = t_0
    else if (z <= (-1.3d-131)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.5d-197)) then
        tmp = y * 4.0d0
    else if (z <= (-2.45d-262)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.9d-284)) then
        tmp = y * 4.0d0
    else if (z <= 3.6d-205) then
        tmp = x * (-3.0d0)
    else if (z <= 0.63d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -4800.0) {
		tmp = t_1;
	} else if (z <= -2.5e-69) {
		tmp = t_0;
	} else if (z <= -1.3e-131) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-197) {
		tmp = y * 4.0;
	} else if (z <= -2.45e-262) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-205) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -4800.0:
		tmp = t_1
	elif z <= -2.5e-69:
		tmp = t_0
	elif z <= -1.3e-131:
		tmp = x * -3.0
	elif z <= -2.5e-197:
		tmp = y * 4.0
	elif z <= -2.45e-262:
		tmp = x * -3.0
	elif z <= -1.9e-284:
		tmp = y * 4.0
	elif z <= 3.6e-205:
		tmp = x * -3.0
	elif z <= 0.63:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -4800.0)
		tmp = t_1;
	elseif (z <= -2.5e-69)
		tmp = t_0;
	elseif (z <= -1.3e-131)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.5e-197)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.45e-262)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.9e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.6e-205)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -4800.0)
		tmp = t_1;
	elseif (z <= -2.5e-69)
		tmp = t_0;
	elseif (z <= -1.3e-131)
		tmp = x * -3.0;
	elseif (z <= -2.5e-197)
		tmp = y * 4.0;
	elseif (z <= -2.45e-262)
		tmp = x * -3.0;
	elseif (z <= -1.9e-284)
		tmp = y * 4.0;
	elseif (z <= 3.6e-205)
		tmp = x * -3.0;
	elseif (z <= 0.63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4800.0], t$95$1, If[LessEqual[z, -2.5e-69], t$95$0, If[LessEqual[z, -1.3e-131], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.5e-197], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.45e-262], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.9e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.6e-205], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.63], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4800 or 0.630000000000000004 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 95.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -4800 < z < -2.50000000000000017e-69 or 3.5999999999999998e-205 < z < 0.630000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.0%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 64.0%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -2.50000000000000017e-69 < z < -1.29999999999999998e-131 or -2.5000000000000001e-197 < z < -2.4500000000000001e-262 or -1.8999999999999999e-284 < z < 3.5999999999999998e-205

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.29999999999999998e-131 < z < -2.5000000000000001e-197 or -2.4500000000000001e-262 < z < -1.8999999999999999e-284

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.4%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 78.8%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 78.8%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 78.8%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4800:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-276}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -0.65)
     t_0
     (if (<= z -2.5e-66)
       (* y 4.0)
       (if (<= z -5.5e-133)
         (* x -3.0)
         (if (<= z -6.7e-198)
           (* y 4.0)
           (if (<= z -8e-265)
             (* x -3.0)
             (if (<= z -1.46e-276)
               (* y 4.0)
               (if (<= z 2.2e-203)
                 (* x -3.0)
                 (if (<= z 14.5) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -2.5e-66) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-133) {
		tmp = x * -3.0;
	} else if (z <= -6.7e-198) {
		tmp = y * 4.0;
	} else if (z <= -8e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.46e-276) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-203) {
		tmp = x * -3.0;
	} else if (z <= 14.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-2.5d-66)) then
        tmp = y * 4.0d0
    else if (z <= (-5.5d-133)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.7d-198)) then
        tmp = y * 4.0d0
    else if (z <= (-8d-265)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.46d-276)) then
        tmp = y * 4.0d0
    else if (z <= 2.2d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 14.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -2.5e-66) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-133) {
		tmp = x * -3.0;
	} else if (z <= -6.7e-198) {
		tmp = y * 4.0;
	} else if (z <= -8e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.46e-276) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-203) {
		tmp = x * -3.0;
	} else if (z <= 14.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -0.65:
		tmp = t_0
	elif z <= -2.5e-66:
		tmp = y * 4.0
	elif z <= -5.5e-133:
		tmp = x * -3.0
	elif z <= -6.7e-198:
		tmp = y * 4.0
	elif z <= -8e-265:
		tmp = x * -3.0
	elif z <= -1.46e-276:
		tmp = y * 4.0
	elif z <= 2.2e-203:
		tmp = x * -3.0
	elif z <= 14.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -2.5e-66)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.5e-133)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.7e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= -8e-265)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.46e-276)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.2e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 14.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	tmp = 0.0;
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -2.5e-66)
		tmp = y * 4.0;
	elseif (z <= -5.5e-133)
		tmp = x * -3.0;
	elseif (z <= -6.7e-198)
		tmp = y * 4.0;
	elseif (z <= -8e-265)
		tmp = x * -3.0;
	elseif (z <= -1.46e-276)
		tmp = y * 4.0;
	elseif (z <= 2.2e-203)
		tmp = x * -3.0;
	elseif (z <= 14.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -2.5e-66], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.5e-133], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.7e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8e-265], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.46e-276], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.2e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 14.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022 or 14.5 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 55.9%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around inf 42.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot \left(0.6666666666666666 - z\right)}{x}\right)} \]

   7. Taylor expanded in z around inf 53.4%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]

   if -0.650000000000000022 < z < -2.49999999999999981e-66 or -5.49999999999999977e-133 < z < -6.69999999999999982e-198 or -7.99999999999999988e-265 < z < -1.45999999999999994e-276 or 2.2e-203 < z < 14.5

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.4%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 64.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 63.2%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 63.2%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 63.2%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -2.49999999999999981e-66 < z < -5.49999999999999977e-133 or -6.69999999999999982e-198 < z < -7.99999999999999988e-265 or -1.45999999999999994e-276 < z < 2.2e-203

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 70.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 70.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 70.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 70.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 70.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 70.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 70.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 70.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 70.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-276}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+77} \lor \neg \left(x \leq 0.3\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+77) (not (<= x 0.3)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+77) || !(x <= 0.3)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.8d+77)) .or. (.not. (x <= 0.3d0))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+77) || !(x <= 0.3)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+77) or not (x <= 0.3):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+77) || !(x <= 0.3))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e+77) || ~((x <= 0.3)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+77], N[Not[LessEqual[x, 0.3]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000003e77 or 0.299999999999999989 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 84.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 84.5%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 84.5%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 84.5%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 84.5%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 84.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 84.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 84.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 84.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 84.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 84.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 84.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 84.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if -5.8000000000000003e77 < x < 0.299999999999999989

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.2%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 75.3%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+77} \lor \neg \left(x \leq 0.3\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+77} \lor \neg \left(x \leq 13.8\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+77) (not (<= x 13.8)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+77) || !(x <= 13.8)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.8d+77)) .or. (.not. (x <= 13.8d0))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+77) || !(x <= 13.8)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e+77) or not (x <= 13.8):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (-6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e+77) || !(x <= 13.8))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e+77) || ~((x <= 13.8)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (-6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e+77], N[Not[LessEqual[x, 13.8]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000001e77 or 13.800000000000001 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 84.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 84.5%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 84.5%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 84.5%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 84.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 84.5%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 84.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 84.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 84.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 84.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 84.6%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 84.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 84.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 84.6%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 84.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if -3.8000000000000001e77 < x < 13.800000000000001

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.4%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+77} \lor \neg \left(x \leq 13.8\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.52) (+ x (* (- y x) 4.0)) (* z (* -6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.52d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((-6.0d0) * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.52:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * (-6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.52)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(-6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.52)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * (-6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 95.0%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.57999999999999996 < z < 0.52000000000000002

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 97.7%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.52000000000000002 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 94.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 94.7%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*r* 94.8%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   8. Simplified 94.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.52) (+ (* x -3.0) (* y 4.0)) (* z (* -6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.52d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((-6.0d0) * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.52:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * (-6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.52)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(-6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.52)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * (-6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 95.0%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.55000000000000004 < z < 0.52000000000000002

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.4%

      \[\leadsto x + \color{blue}{\left(-6 \cdot x + 6 \cdot y\right)} \cdot \left(0.6666666666666666 - z\right) \]

   6. Taylor expanded in z around 0 97.2%

      \[\leadsto \color{blue}{x + 0.6666666666666666 \cdot \left(-6 \cdot x + 6 \cdot y\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 97.2%

         \[\leadsto x + \color{blue}{\left(0.6666666666666666 \cdot \left(-6 \cdot x\right) + 0.6666666666666666 \cdot \left(6 \cdot y\right)\right)} \]

      2. associate-+r+ 97.2%

         \[\leadsto \color{blue}{\left(x + 0.6666666666666666 \cdot \left(-6 \cdot x\right)\right) + 0.6666666666666666 \cdot \left(6 \cdot y\right)} \]

      3. associate-*r* 97.5%

         \[\leadsto \left(x + \color{blue}{\left(0.6666666666666666 \cdot -6\right) \cdot x}\right) + 0.6666666666666666 \cdot \left(6 \cdot y\right) \]

      4. metadata-eval 97.5%

         \[\leadsto \left(x + \color{blue}{-4} \cdot x\right) + 0.6666666666666666 \cdot \left(6 \cdot y\right) \]

      5. distribute-rgt1-in 97.5%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + 0.6666666666666666 \cdot \left(6 \cdot y\right) \]

      6. *-commutative 97.5%

         \[\leadsto \color{blue}{x \cdot \left(-4 + 1\right)} + 0.6666666666666666 \cdot \left(6 \cdot y\right) \]

      7. metadata-eval 97.5%

         \[\leadsto x \cdot \color{blue}{-3} + 0.6666666666666666 \cdot \left(6 \cdot y\right) \]

      8. associate-*r* 97.7%

         \[\leadsto x \cdot -3 + \color{blue}{\left(0.6666666666666666 \cdot 6\right) \cdot y} \]

      9. metadata-eval 97.7%

         \[\leadsto x \cdot -3 + \color{blue}{4} \cdot y \]

      10. *-commutative 97.7%

          \[\leadsto x \cdot -3 + \color{blue}{y \cdot 4} \]

   8. Simplified 97.7%

      \[\leadsto \color{blue}{x \cdot -3 + y \cdot 4} \]

   if 0.52000000000000002 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 94.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 94.7%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*r* 94.8%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   8. Simplified 94.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-16} \lor \neg \left(x \leq 2.3 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e-16) (not (<= x 2.3e+15))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-16) || !(x <= 2.3e+15)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.8d-16)) .or. (.not. (x <= 2.3d+15))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-16) || !(x <= 2.3e+15)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e-16) or not (x <= 2.3e+15):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e-16) || !(x <= 2.3e+15))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.8e-16) || ~((x <= 2.3e+15)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e-16], N[Not[LessEqual[x, 2.3e+15]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999991e-16 or 2.3e15 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. cancel-sign-sub-inv 79.4%

         \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. *-commutative 79.4%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

      4. cancel-sign-sub-inv 79.4%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

      5. distribute-lft-neg-in 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

      6. *-commutative 79.4%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

      7. distribute-lft-neg-in 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

      8. metadata-eval 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

      9. sub-neg 79.4%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      10. distribute-lft-in 79.5%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

      11. metadata-eval 79.5%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

      12. neg-mul-1 79.5%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      13. *-commutative 79.5%

          \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

      14. associate-*l* 79.5%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

      15. associate-+r+ 79.5%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

      16. metadata-eval 79.5%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      17. *-commutative 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      18. associate-*l* 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      19. metadata-eval 79.5%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 38.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 38.6%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.79999999999999991e-16 < x < 2.3e15

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 77.9%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 37.4%

      \[\leadsto \color{blue}{4 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto \color{blue}{y \cdot 4} \]

   9. Simplified 37.4%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-16} \lor \neg \left(x \leq 2.3 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.5%

   \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]
6. Add Preprocessing

Alternative 14: 25.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 49.9%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. metadata-eval 49.9%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right)} \cdot \left(0.6666666666666666 - z\right)\right) \]

   2. cancel-sign-sub-inv 49.9%

      \[\leadsto x \cdot \color{blue}{\left(1 - 6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   3. *-commutative 49.9%

      \[\leadsto x \cdot \left(1 - \color{blue}{\left(0.6666666666666666 - z\right) \cdot 6}\right) \]

   4. cancel-sign-sub-inv 49.9%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(0.6666666666666666 - z\right)\right) \cdot 6\right)} \]

   5. distribute-lft-neg-in 49.9%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\left(0.6666666666666666 - z\right) \cdot 6\right)}\right) \]

   6. *-commutative 49.9%

      \[\leadsto x \cdot \left(1 + \left(-\color{blue}{6 \cdot \left(0.6666666666666666 - z\right)}\right)\right) \]

   7. distribute-lft-neg-in 49.9%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   8. metadata-eval 49.9%

      \[\leadsto x \cdot \left(1 + \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right)\right) \]

   9. sub-neg 49.9%

      \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

   10. distribute-lft-in 49.9%

       \[\leadsto x \cdot \left(1 + \color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)}\right) \]

   11. metadata-eval 49.9%

       \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + -6 \cdot \left(-z\right)\right)\right) \]

   12. neg-mul-1 49.9%

       \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

   13. *-commutative 49.9%

       \[\leadsto x \cdot \left(1 + \left(-4 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right)\right) \]

   14. associate-*l* 49.9%

       \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right)\right) \]

   15. associate-+r+ 49.9%

       \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-6 \cdot z\right) \cdot -1\right)} \]

   16. metadata-eval 49.9%

       \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

   17. *-commutative 49.9%

       \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

   18. associate-*l* 49.9%

       \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

   19. metadata-eval 49.9%

       \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

7. Simplified 49.9%

   \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

8. Taylor expanded in z around 0 25.2%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 25.2%

      \[\leadsto \color{blue}{x \cdot -3} \]

10. Simplified 25.2%

    \[\leadsto \color{blue}{x \cdot -3} \]

11. Final simplification 25.2%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Alternative 15: 2.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 52.6%

   \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

6. Taylor expanded in x around inf 2.9%

   \[\leadsto \color{blue}{x} \]

7. Final simplification 2.9%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024050 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))